Problem 4 - College Algebra Essentials

Question

Write each equation in its equivalent exponential form. $$2=\log _{9} x$$

Step-by-Step Solution

Answer

The equivalent exponential form of the logarithmic equation \(2=\log _{9} x\) is \(9^2 = x\).

Step 1: Understanding the Logarithm and Its Components

First, we need to understand the structure of the logarithm in the equation \(2=\log _{9} x\). Here, the base of the logarithm is '9', the value of the entire logarithm is '2' and 'x' is the number whose logarithm is taken.

Step 2: Conversion of Logarithmic to Exponential Form

After understanding the components of the logarithm, apply the definition of the logarithm to convert it into the exponential form. This will give us \(9^2 = x\) as the equivalent exponential form.